I don't have that much of a slope, but when it's icy it can be significant, and even a tug has a tough time. A few years back, in the winter, I relied on a 12v Harbor Freight remote control winch. It was cheap at about $60, but really kind of sucked overall.

Just recently, to help the girls out all year, and for me in the winter when it's icy, I just got done putting together a new system.

I bought the same Harbor Freight hoist that others are talking about. It's $129.99 and I got it at 25% off of that on the last big sale. So under $100.
It does have a handheld cord that you could extend. It runs on 110V and is actually made very well. It feeds about 32 feet per minute. It has a hard stop that will shut it down if it gets pulled all the way in. You could attach a lead on to the hook so that the winch will stop for sure before the plane hits the winch. (I'm calling it a winch but at Harbor Freight it's technically a "Hoist")

What I did to mine is a bit different. I bought a Linksprite R4. (Think Arduino, with built in wifi and 4 relays). I set it up to be run via a web page (internal only) from my iphone, with various runtimes. So I can hit a button and extend the cable 45 seconds, for instance. Then I can hook it up, and hit another button to retract for various times, from .5 seconds to 30 seconds. I can also hit STOP at any point and shut it off. But this way I can feed it 10 seconds of retract if I want, or 5, or 2, or whatever, so it goes slow if needed. It all runs on the wifi at the hangar.

I'm guessing that some of the winch remotes could be modified similarly, or you could simply extend the control cord.

Anyway, it's not a "perfect" option since it doesn't come with a wireless remote, but you can certainly improvise with it and from a mechanical standpoint it's cheap and solid. I'd love to have a tractor but in a T-hangar it's just one more thing to get in the way and to maintain, for me.
The tugs are definitely expensive. I have 2 types of tugs, and neither is ideal.
The one from WagAero can do a reasonable job pushing planes around and can be connected remotely. The other is I think a minimax, and that one is more of a pain to manually hook up but is much smaller and lighter. Neither one does a good job of turning, so they both aren't fantastic. That's why I went the winch route for the girls. I want to guarantee that the wife and daughter can get the plane back in the hangar anytime they need to, and that will do the trick for sure.

My existing pole barn hangar is 36' wide outside, about 34'-6" clear width inside. Fine for the 6A - I can taxi straight in, shut down, and do a 3-point turn or a 180 in place and not bump anything, ready to taxi out under power the next time. The -10 will pose a challenge. The front inboard posts that bear the weight load of the overhead door tracks will have to be cut to allow small doors for the wingtips to pass through. The overhead beam that carries the door weight will need to be extended all the way to the corner posts so the inboard front posts are no longer load-bearing.

This mod will gain me some extra clearance, but not more than 12" on each wingtip. I foresee things being too tight inside the 36x48 hangar to do any kind of 3-, 4-,5- or 6 point turn to get her facing out again. The idea of dragging it in by the tail or pushing it in by the nose wheel is appealing. I don't see a way to get the gear up on casters for maneuvering inside the hangar without damaging wheel pants in the process. Something would eventually go wrong.

I could re-design my hangar to put a door in the 48' side and close the front off, but that would involve retrofitting quite a beefy header to carry roof snow loads as well as rolling door weight, plus a new fairly steep ramp - not the preferred way to go. I'm pondering ways I can modify the tail tie down at this stage of construction to make it up to the task of winching the plane in tail-first on a very shallow turf incline.

Tim brought up a point that I had been thinking about. For those using the modified snow blowers, how are they for turning?

I have to do a couple S-Turns to get my 10 back in the hangar, so I can't just push it straight into the hangar. Too many obstacles in the way.

Bob, You bring up the one slight nuisance of the snow blower method. The steering is done by slight lifting and turning of the blowers handles. This reduces the downward pressure of the tires and they lose traction allowing you to turn it pretty easily. A castering wheel would be nice but since I only have to push the -10 straight back with minor turns for alignment, it isn't a big deal.

I purchased an electric wheelchair off Craigslist. New batteries and was into it about $250. Took seat off, put on a simple handle and a cradle for tailwheel where the step was located. Works great for the Bearhawk which is pretty heavy to move by myself, for my RV-4 it is so light a tow bar is easier.

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